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Effect of metallic melt on the viscosity of peridotite
Earth and Planetary Science Letters 260 (2007) 355 – 360 www.elsevier.com/locate/epsl
Effect of metallic melt on the viscosity of peridotite Justin Hustoft ⁎, Ted Scott, David L. Kohlstedt ⁎ University of Minnesota, Department of Geology and Geophysics, 310 Pillsbury Dr SE, Minneapolis, MN 55455, United States Received 6 November 2006; received in revised form 3 June 2007; accepted 3 June 2007 Available online 12 June 2007 Editor: G.D. Price
Abstract To examine the dependence of viscosity of a partially molten peridotite on the wetting nature of the melt phase, we combine previously published measurements of diffusion creep on samples of olivine + MORB with new results from our creep experiments on samples of olivine + Fe–S and samples of olivine + Au. For these three partially molten systems, the melt-solid dihedral angle varies from θ = 38° for olivine + MORB to θ = 90° for olivine + Fe–S to θ = 150° for olivine + Au. In each case, the viscosity, η, decreases with increasing melt fraction, ϕ, according to the relation η ∝ exp(− αϕ). Our results reveal a substantial change in the value of the material-dependent parameter α, from α = 21 for MORB in an olivine aggregate (with θ b 60°) to α = 4 ± 1 for the two metallic melts in polycrystalline olivine (both with θ N 60°). For a melt fraction of 0.05, this difference in α corresponds to more than a factor of two higher viscosity for samples composed of olivine + a metallic melt relative to the viscosity of samples of olivine + MORB. This difference in viscosity can be attributed to two factors: (i) The enhancement of grain-scale stress due to the presence of melt is smaller for the metallic melt than for the basaltic melt because the melt-solid contact area decreases with increasing θ, and (ii) the flux of olivine through the metallic melt is small due to the low solubility of olivine in the non-silicate melts. © 2007 Elsevier B.V. All rights reserved. Keywords: creep; viscosity; metallic melt; olivine
1. Introduction The dependence of strain rate on melt fraction is encompassed in the parameter α in the flow law reported for creep experiments on olivine + mid-ocean ridge basalt (MORB) (Keleman et al., 1997; Hirth and Kohlstedt, 2003; Zimmerman and Kohlstedt, 2004; Scott and Kohlstedt, 2006) n e ¼ A rm expða/Þexp Q ð1Þ RT d ⁎ Corresponding authors. Tel.: +1 612 626 0572; fax: +1 612 625 3819. E-mail addresses: [email protected] (J. Hustoft), [email protected] (D.L. Kohlstedt). 0012-821X/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2007.06.011
where ε˙ is strain rate, σ is differential stress with n the stress exponent, d is grain size with m the grain size exponent, ϕ is melt fraction, Q is activation energy, R is the ideal gas constant, and T is absolute temperature. Although melt fraction has a marked effect on strain rate, little is known about the relationship between α and material parameters such as dihedral angle, θ. In this study, we have investigated the effect of θ and ϕ on the viscosity of dry, partially molten peridotite deformed in the diffusion creep regime. Two metallic melt phases were used in order to investigate a range of dihedral angles: (1) Fe–FeS (Fe–S) with θ ≈ 90° and a dynamic viscosity μ = 0.04 Pa s (Terasaki et al., 2001) and (2) Au with θ ≈ 150° and μ = 0.003 Pa s (Tucker and Weisberg, 1986). Representative micrographs of these solid–melt
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We have investigated the effect of iron sulfide and gold melts on the viscosity of peridotite in order to characterize the effect of a non-wetting, metallic melt phase on the viscosity of peridotite. By comparing the effect of MORB to the effect of these non-wetting metallic melts on the viscosity of peridotite, we can examine the influences of both the local stress enhancement at grain contacts and the solubility of olivine in the melt phase on the viscosity of the aggregate. Our low-strain experiments (ε b 0.15) provide essential information concerning the effect of melt on rheological properties at a given melt fraction. This information is required to analyze the flow behavior in large-strain experiments in which melt segregates during deformation (Holtzman et al., 2003a,b; Hustoft and Kohlstedt, 2006; Groebner and Kohlstedt, 2006). The data presented in this paper are a baseline for interpreting the results of higher strain experiments in which melt segregates by constraining the viscosity of both the melt-rich and the melt-depleted regions. The results from our compressive creep experiments may be applicable to regions such as the core–mantle
Fig. 1. Secondary electron micrographs of (a) an undeformed and (b) a deformed sample of olivine (dark gray) with 5 vol.% Fe–S (light gray) distributed as isolated pockets in triple junctions.
systems are shown in Figs. 1 and 2. Creep results for these systems are compared to previous results from studies using MORB, for which θ ≈ 38° and μ = 150 Pa s (Shaw et al., 1968). For MORB in an olivine matrix, the median dihedral angle is θ b 60°; that is, the melt phase wets triple junctions. In addition, MORB wets some of the grain boundaries even at small melt fractions as a result of the anisotropy in interfacial energy of olivine grains (Cooper and Kohlstedt, 1982). For metallic melts such as Fe–S and Au in olivine matrices, the median dihedral angle is θ N 60°; that is, these melts are non-wetting in a silicate matrix. As a result of the high solid-melt interfacial energies for these systems, the metallic melts tend to remain in isolated pockets in grain boundaries, triple junctions, and four-grain corners. However, results from Yoshino et al. (2003, 2004) and Hustoft and Kohlstedt (2006) reveal that, in the case of Fe–S in olivine (θ = 90°), the metallic melt resides in a network when ϕ ≥ 0.05. The threshold melt fraction for interconnection of Au melts in olivine (θ = 150°) is expected to be ϕ = 0.20 (Bulau et al., 1979), though this value has not been experimentally tested.
Fig. 2. Secondary electron micrograph of deformed samples of olivine (dark gray) with (a) 5 vol.% and (b) 20 vol.% Au (light gray). The Au is primarily present at triple junctions.
J. Hustoft et al. / Earth and Planetary Science Letters 260 (2007) 355–360
357
Table 1 Composition, experimental conditions and results of compressive creep experiments . Sample Composition T (K) r (MPa) e (10–5 S−1 )
df (μm)
ε
n
PI-1259
Olivine + 0.01 Fe–S
6.7 ± 0.4
0.03
0.8
PI-1257
Olivine + 0.09 Fe–S
8.1 ± 0.4
0.08
1.2
PI-1249
Olivine + 0.20 Fe–S
1523
7.3 ± 0.4
0.10
1.0
PI-1279
Olivine + 0.05 Au
4.2 ± 0.3
0.12
1.2
PI-1287
Olivine + 0.20 Au
1471 1471 1471 1521 1521 1521 1523
6±1
0.09
1.1
1508 1519 1519 1519 1519 1523
10 35 16 72 124 10 28 51 100 15 35 6 14 38 80 120 7 14 67 140 36 78 136 17 49 64
boundary, an environment where metallic melt rather than silicate melt is likely to affect the viscosity of the lower mantle. In addition, understanding the interaction of a metallic melt with a silicate mantle is necessary for modeling the initial conditions of core formation. If the core grew by percolation of metallic melt through the mantle (Hustoft and Kohlstedt, 2006), to model accurately this system, it is important to know the effect of a metallic melt on the viscosity of silicate rocks before the core-composition fluids segregated from the silicate mantle (Hier-Majumder et al., 2006).
0.5 1.3 0.5 2.1 3.0 0.5 1.7 3.0 5.4 0.5 1.4 0.7 1.6 3.7 8.4 15 0.6 0.5 2.5 6.1 4.5 11 25 4.5 15 22
formed at constant applied load for a range of differential stress from 5 to 140 MPa and strain rates from 10− 6 to 10− 4 s− 1 at temperatures of 1473 to 1523 K and a
2. Experimental methods Details of the experimental methods are reported in Hustoft and Kohlstedt (2006) and Scott and Kohlstedt (2006); the main points are summarized here. Samples were synthesized from San Carlos olivine (Fo90) with d ≤ 10 μm and reagent grade powders of Fe, FeS, and Au. All powders were pre-dried in a 1 atm furnace at 1273 K for 10 h. Samples of olivine with 0.01, 0.09 and 0.20 Fe–S with Fe:S = 2:1 by volume and 0.05 and 0.20 Au by volume were hot-pressed in a gas-medium apparatus at 1523 K for 4 h prior to deformation. All triaxial compression (pure shear) experiments were per-
Fig. 3. Log–log plot of strain rate versus stress for samples of olivine + Fe–S. The flow law for diffusion creep of melt-free aggregates of olivine (Hirth and Kohlstedt, 2003) is plotted for comparison to the results from samples with Fe–S melt.
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confining pressure of 300 MPa. The total strain in each experiment was limited to ε b 0.15 (Table 1). 3. Experimental results Scanning electron microscopy (SEM) images illustrating the distribution of Fe–S melt before and after deformation are presented in Fig. 1. SEM images revealing the distribution of Au in two deformed samples are shown in Fig. 2. The distribution of the metallic melt phases is not substantially changed by deformation. No significant segregation or preferred orientation of the metallic melt phase develops during our low-strain, compressive-creep experiments; in contrast, pronounced melt segregation and melt preferred orientation form in similar samples deformed to high strains in simple shear (Groebner and Kohlstedt, 2006; Hustoft and Kohlstedt, 2006). Experimental results are plotted as strain rate versus differential stress for samples of olivine + Fe–S and olivine + Au in Figs. 3 and 4, respectively. Best fits to the data yield n = 0.8 to 1.2, indicating that all samples were deformed in the diffusion creep regime. Strain rates were normalized to a common grain size of d = 8 μm and a common temperature of T = 1523 K using Eq. (1) with m = 3 and Q = 375 kJ mol− 1, values appropriate for the diffusion creep regime (Hirth and Kohlstedt, 2003; Zimmerman and Kohlstedt, 2004). In addition, the flow law determined by Hirth and Kohlstedt (2003) for diffusion creep of samples of melt-free olivine (ϕ = 0) with d = 8 μm and T = 1523 K is shown for comparison.
Fig. 5. Viscosity for samples of olivine plus Fe–S and Au melt normalized by the viscosity of melt-free dunite plotted against melt fraction. Values of viscosity are calculated from the data in Figs. 3 and 4; the viscosity for melt-free olivine is from Hirth and Kohlstedt (2003). A least-squares fit of the data to Eq. (2) yields α = 4 ± 1. A least squares fit of the data to Eq. (3) yields k = 1.4. For comparison, viscosity is plotted versus melt fraction based on Eq. (2) with α = 21, a value appropriate for aggregates of partially molten lherzolite and olivine plus MORB (Zimmerman and Kohlstedt, 2004; Scott and Kohlstedt, 2006). The effect of Au melt on viscosity of peridotite is not distinguishable from that of Fe–S melt.
The dependence of viscosity on the fraction of metallic melt is illustrated in Fig. 5. Effective viscosity is plotted versus melt fraction for samples containing molten Fe–S and samples containing molten Au using all the stress–strain rate data from Figs. 3 and 4. The enhancement of viscosity is determined by plotting the ratio of the measured viscosity to the viscosity for a melt-free (ϕ = 0) sample as calculated from Eq. (1). A value of α for samples of olivine + Fe–S and olivine + Au was determined from a least-squares fit to these data using Eq. (2): g/ ¼ expða/Þ g/¼0
ð2Þ
4. Discussion
Fig. 4. Log–log plot of stress versus strain rate for samples of olivine + Au. The diffusion creep flow law for melt-free samples from Hirth and Kohlstedt (2003) is plotted for comparison to the results from samples with Au melt.
The SEM micrographs in Figs. 1 and 2 illustrate that the distribution of molten Fe–S and Au, respectively, in an olivine aggregate is essentially unchanged by lowstrain (ε b 0.15), compressive creep deformation of the samples. In contrast, a significant melt segregation occurs and a pronounced melt preferred orientation develops during large-strain (ε N 1) experiments (Hustoft and Kohlstedt, 2006; Groebner and Kohlstedt, 2006). The stress versus strain rate data for samples of olivine + 20 vol.% of a metallic melt (Fe–S or Au) plot between the flow law for melt-free olivine and the flow law for olivine + 10 vol.% MORB deforming by diffusion creep (stress exponent n ≈ 1). This fact indicates that a metallic
J. Hustoft et al. / Earth and Planetary Science Letters 260 (2007) 355–360
melt has a significantly smaller effect on strain rate than does a silicate melt, such as MORB. More precisely, the value of α = 4 ± 1 determined from Fig. 5 for samples of olivine plus a metallic melt with h N 60° is approximately one-fifth of the value of α = 21 reported for samples of partially molten lherzolite (Zimmerman and Kohlstedt, 2004) and samples of olivine plus MORB (Scott and Kohlstedt, 2006), both melt-solid systems with h b 60°. The causes for the enhancement in strain rate that results from the presence of a melt phase must be examined to explain this difference. The presence of melt influences the viscosity of a partially molten rock (i) by causing a local enhancement in stress at grain–grain contacts and (ii) by providing a shortcircuit diffusion path (Cooper et al., 1989). The local enhancement in stress at grain boundaries is a result of the reduced contact area between grains due to the presence of melt between grains. Melt does not transmit shear stress; therefore, the local stress felt at a melt-bordered grain– grain contact is increased relative to that experienced at a boundary with no reduction in contact area due to the presence of melt. For samples of olivine plus MORB, both processes are important. In contrast, for samples of olivine plus metallic melt, the metallic melt almost certainly does not act as an effective short-circuit diffusion path because the solubility of olivine in and thus the flux of olivine through the metallic phase will be very small. Therefore, the primary effect of the metallic melt on viscosity will be through its role in enhancing the local stress felt by grains. This stress enhancement effect is significantly smaller for a metallic melt than for a silicate melt because these two types of melt have significantly different wetting geometries. Metallic melts are present as isolated, nearly spherical pockets confined primarily to triple junctions and four-grain junctions, while silicate melts wet all of the triple junctions and some of the grain boundaries even at low values of ϕ. The distribution of the metallic melt throughout the silicate matrix suggests that metallic melts in an olivine aggregate can be modeled as a weak phase distributed throughout a stronger load-bearing network (Tharp, 1983; Hirth and Kohlstedt, 1995). The relationship between the strength of the porous material σφ and the strength of the solid aggregate r0 is expressed by r/ ¼ 1 k/2=3 r0
ð3Þ
where k is an empirically determined constant generally valued between 0.98 and 2.26 (Tharp, 1983; Hirth and Kohlstedt, 1995). With a value of k = 1.4, Eq. (3) yields a good fit to the data in Fig. 5.
359
The results of this study indicate that, for melt-solid systems with θ N 60°, strain rate and viscosity are insensitive to dihedral angle. This behavior is very different from that expected for melt–solid systems with θ b 60° for which viscosity is predicted to decrease with decreasing dihedral angle for a given melt fraction (Cooper et al., 1989). Therefore, because the dihedral angle of molten iron sulfide in a silicate matrix decreases with increasing oxygen fugacity (Minarik et al., 1996; Gaetani and Grove, 1999), in a higher oxygen fugacity environment such as the martian mantle (Rubie et al., 2004), the dihedral angle in the olivine + Fe–S system may be b60° such that this metallic melt could produce a significantly larger reduction in viscosity than observed in our experiments. Likewise, the dihedral angle of an Fe–S melt in contact with a high pressure silicate phase, such as perovskite, can approach and even drop below 60° (Minarik et al., 1996; Shannon and Agee, 1998; Takafuji et al., 2004) such that the effect of an Fe–S melt on viscosity will be substantial. 5. Conclusions For a given melt fraction, the presence of a metallic melt has a significantly smaller effect on the viscosity of a partially molten silicate rock than does MORB for the conditions of our experiments (T ≈ 1473 K, P = 300 MPa, f02= Ni:NiO). In the diffusion creep regime, the addition of 10 vol.% MORB melt decreases the viscosity by nearly an order of magnitude, while the addition of 10 vol.% metallic melt decreases the viscosity by less than a factor of 2. For the olivine + metallic melt system, the value of α in the relation is g/ /g/=0 = exp(–a/) is ∼ 1/5th that for the olivine + MORB system. The decrease in viscosity for an aggregate composed of one or more solid phases plus a melt phase at a given melt fraction is controlled by the level of solubility of solid in the melt, and hence the flux of solid through the melt, as well as by the geometry/distribution of the melt. For relatively insoluble systems, the decrease in viscosity due to the presence of a melt phase is low, but still measurable due to local stress enhancement at grain– grain junctions. Therefore, knowledge of the level of solubility of the minerals in the melt combined with information on the melt topology allows for a priori estimation of the viscosity via the parameter α. Acknowledgments We thank Mark Zimmerman for assistance with experiments and discussions. This study was supported
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by NSF grant OCE-0327143 (basalt melt) and NASA PG&G grant NNG04G173G (metallic melts). References Bulau, J.R., Waff, H.S., Tyburczy, J.A., 1979. Mechanical and thermodynamic constraints on fluid distribution in partial melts. J. Geophys. Res. 84 (B11), 6102–6108. Cooper, R.F., Kohlstedt, D.L., 1982. Interfacial energies in the olivine–basalt system, in high-pressure research. In: Akimota, S., Manghnani, M.H. (Eds.), Geophysics, Advances in Earth and Planetary Sciences, vol. 12. Center for Academic Publications, Tokyo, pp. 217–228. Cooper, R.F., Kohlstedt, D.L., Chyung, K., 1989. Solution-precipitation enhanced creep in solid–liquid aggregates which display a non-zero dihedral angle. Acta Met. 37, 1759–1771. Gaetani, G.A., Grove, T.L., 1999. Wetting of olivine by sulfide melt: implications for Re/Os ratios in mantle peridotite and late-stage core formation. Earth Planet. Sci. Lett. 169, 147–163. Groebner, N., Kohlstedt, D.L., 2006. Deformation induced metal melt networks in silicates: implications for core–mantle interactions in planetary bodies. Earth Planet. Sci. Lett. 245, 571–580. Hier-Majumder, C.A., Hustoft, J.W., Solomon, S.C., 2006. Core formation by percolation of iron-rich liquids. Lunar and Planetary Science, vol. XXXVII. Abstract #1329. Hirth, G., Kohlstedt, D.L., 1995. Experimental constraints on the dynamics of the partially molten upper mantle 2. Deformation in the dislocation creep regime. J. Geophys. Res. 100, 15441–15449. Hirth, G., Kohlstedt, D.L., 2003. Rheology of the upper mantle and the mantle wedge: a view from the experimentalists. In: Eiler, J.M. (Ed.), Inside the Subduction Factory, AGU Geophysical Monograph, vol. 138. AGU Press. Holtzman, B.K., Groebner, N.J., Zimmerman, M.E., Ginsberg, S.B., Kohlstedt, D.L., 2003a. Stress-driven melt segregation in partially molten rocks. Geochem. Geophys. Geosyst. 4 (5), 8607. doi:10.1029/2001GC000258 _______________________. Holtzman, B.K., Kohlstedt, D.L., Zimmerman, M.E., Heidelbach, F., Hiraga, T., Hustoft, J., 2003b. Melt segregation and strain partitioning: implications for seismic anisotropy and mantle flow. Science 301, 1227–1230.
Hustoft, J., Kohlstedt, D.L., 2006. Metal-silicate segregation in deforming dunitic rocks. Geochem. Geophys. Geosyst. 7 (Q02001). doi:10.1029/2005GC001048 _______________________. Keleman, P.B., Hirth, G., Shimizu, N., Spiegelman, M., Dick, H.J.B., 1997. A review of melt migration processes in the adiabatically upwelling mantle beneath oceanic spreading ridges. Philos. Trans. R. Soc. Lond., A 355, 283–318. Minarik, W.G., Ryerson, F.J., Watson, E.B., 1996. Textural entrapment of core-forming melts. Science 272, 530–533. Rubie, D.C., Gessmann, C.K., Frost, D.J., 2004. Partitioning of oxygen during core formation on the Earth and Mars. Nature 429, 58–61. Scott, T., Kohlstedt, D.L., 2006. The effect of large melt fraction on the deformation behavior of peridotite. Earth Planet. Sci. Lett. 246, 177–187. Shannon, M.C., Agee, C.B., 1998. Percolation of core melts at lower mantle conditions. Science 280, 1059–1061. Shaw, H.R., Wright, T.L., Peck, D.L., Okamura, R.T., 1968. The viscosity of basaltic magma: an analysis of field measurements in Makaopuhi lava lake, Hawaii. Am. J. Sci. 266, 225–264. Takafuji, N., Hirose, K., Ono, S., Xu, F., Mitome, M., Bando, Y., 2004. Segregation of core melts by permeable flow in the lower mantle. Earth Planet. Sci. Lett. 224, 249–257. Terasaki, H., Kato, T., Urakawa, S., Funakoshi, K., Suzuki, A., Okada, T., Maeda, M., Sato, J., Kubo, T., Kasai, S., 2001. The effect of temperature, pressure, and sulfur content on viscosity of the Fe– FeS melt. Earth Planet. Sci. Lett. 190, 93–101. Tharp, T.M., 1983. Analogies between the high-temperature deformation of polyphase rocks and the mechanical behavior of porous powder metal. Tectonophysics 96, T1–T11. Tucker, D.B., Weisberg, A.H., 1986. Planarization of gold and aluminum thin films using a pulsed laser. IEEE Electron Device Lett. EDL-7, 1–4. Yoshino, T., Walter, M.J., Katsura, T., 2003. Core formation in planetesimals triggered by permeable flow. Nature 422, 154–157. Yoshino, T., Walter, M.J., Katsura, T., 2004. Connectivity of molten Fe alloy in peridotite based on in situ electrical conductivity measurements: implications for core formation in terrestrial planets. Earth Planet. Sci. Lett. 222, 625–643. Zimmerman, M., Kohlstedt, D.L., 2004. Rheological properties of partially molten lherzolite. J. Petrol. 45, 275–298.
Effect of metallic melt on the viscosity of peridotite Justin Hustoft ⁎, Ted Scott, David L. Kohlstedt ⁎ University of Minnesota, Department of Geology and Geophysics, 310 Pillsbury Dr SE, Minneapolis, MN 55455, United States Received 6 November 2006; received in revised form 3 June 2007; accepted 3 June 2007 Available online 12 June 2007 Editor: G.D. Price
Abstract To examine the dependence of viscosity of a partially molten peridotite on the wetting nature of the melt phase, we combine previously published measurements of diffusion creep on samples of olivine + MORB with new results from our creep experiments on samples of olivine + Fe–S and samples of olivine + Au. For these three partially molten systems, the melt-solid dihedral angle varies from θ = 38° for olivine + MORB to θ = 90° for olivine + Fe–S to θ = 150° for olivine + Au. In each case, the viscosity, η, decreases with increasing melt fraction, ϕ, according to the relation η ∝ exp(− αϕ). Our results reveal a substantial change in the value of the material-dependent parameter α, from α = 21 for MORB in an olivine aggregate (with θ b 60°) to α = 4 ± 1 for the two metallic melts in polycrystalline olivine (both with θ N 60°). For a melt fraction of 0.05, this difference in α corresponds to more than a factor of two higher viscosity for samples composed of olivine + a metallic melt relative to the viscosity of samples of olivine + MORB. This difference in viscosity can be attributed to two factors: (i) The enhancement of grain-scale stress due to the presence of melt is smaller for the metallic melt than for the basaltic melt because the melt-solid contact area decreases with increasing θ, and (ii) the flux of olivine through the metallic melt is small due to the low solubility of olivine in the non-silicate melts. © 2007 Elsevier B.V. All rights reserved. Keywords: creep; viscosity; metallic melt; olivine
1. Introduction The dependence of strain rate on melt fraction is encompassed in the parameter α in the flow law reported for creep experiments on olivine + mid-ocean ridge basalt (MORB) (Keleman et al., 1997; Hirth and Kohlstedt, 2003; Zimmerman and Kohlstedt, 2004; Scott and Kohlstedt, 2006) n e ¼ A rm expða/Þexp Q ð1Þ RT d ⁎ Corresponding authors. Tel.: +1 612 626 0572; fax: +1 612 625 3819. E-mail addresses: [email protected] (J. Hustoft), [email protected] (D.L. Kohlstedt). 0012-821X/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2007.06.011
where ε˙ is strain rate, σ is differential stress with n the stress exponent, d is grain size with m the grain size exponent, ϕ is melt fraction, Q is activation energy, R is the ideal gas constant, and T is absolute temperature. Although melt fraction has a marked effect on strain rate, little is known about the relationship between α and material parameters such as dihedral angle, θ. In this study, we have investigated the effect of θ and ϕ on the viscosity of dry, partially molten peridotite deformed in the diffusion creep regime. Two metallic melt phases were used in order to investigate a range of dihedral angles: (1) Fe–FeS (Fe–S) with θ ≈ 90° and a dynamic viscosity μ = 0.04 Pa s (Terasaki et al., 2001) and (2) Au with θ ≈ 150° and μ = 0.003 Pa s (Tucker and Weisberg, 1986). Representative micrographs of these solid–melt
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We have investigated the effect of iron sulfide and gold melts on the viscosity of peridotite in order to characterize the effect of a non-wetting, metallic melt phase on the viscosity of peridotite. By comparing the effect of MORB to the effect of these non-wetting metallic melts on the viscosity of peridotite, we can examine the influences of both the local stress enhancement at grain contacts and the solubility of olivine in the melt phase on the viscosity of the aggregate. Our low-strain experiments (ε b 0.15) provide essential information concerning the effect of melt on rheological properties at a given melt fraction. This information is required to analyze the flow behavior in large-strain experiments in which melt segregates during deformation (Holtzman et al., 2003a,b; Hustoft and Kohlstedt, 2006; Groebner and Kohlstedt, 2006). The data presented in this paper are a baseline for interpreting the results of higher strain experiments in which melt segregates by constraining the viscosity of both the melt-rich and the melt-depleted regions. The results from our compressive creep experiments may be applicable to regions such as the core–mantle
Fig. 1. Secondary electron micrographs of (a) an undeformed and (b) a deformed sample of olivine (dark gray) with 5 vol.% Fe–S (light gray) distributed as isolated pockets in triple junctions.
systems are shown in Figs. 1 and 2. Creep results for these systems are compared to previous results from studies using MORB, for which θ ≈ 38° and μ = 150 Pa s (Shaw et al., 1968). For MORB in an olivine matrix, the median dihedral angle is θ b 60°; that is, the melt phase wets triple junctions. In addition, MORB wets some of the grain boundaries even at small melt fractions as a result of the anisotropy in interfacial energy of olivine grains (Cooper and Kohlstedt, 1982). For metallic melts such as Fe–S and Au in olivine matrices, the median dihedral angle is θ N 60°; that is, these melts are non-wetting in a silicate matrix. As a result of the high solid-melt interfacial energies for these systems, the metallic melts tend to remain in isolated pockets in grain boundaries, triple junctions, and four-grain corners. However, results from Yoshino et al. (2003, 2004) and Hustoft and Kohlstedt (2006) reveal that, in the case of Fe–S in olivine (θ = 90°), the metallic melt resides in a network when ϕ ≥ 0.05. The threshold melt fraction for interconnection of Au melts in olivine (θ = 150°) is expected to be ϕ = 0.20 (Bulau et al., 1979), though this value has not been experimentally tested.
Fig. 2. Secondary electron micrograph of deformed samples of olivine (dark gray) with (a) 5 vol.% and (b) 20 vol.% Au (light gray). The Au is primarily present at triple junctions.
J. Hustoft et al. / Earth and Planetary Science Letters 260 (2007) 355–360
357
Table 1 Composition, experimental conditions and results of compressive creep experiments . Sample Composition T (K) r (MPa) e (10–5 S−1 )
df (μm)
ε
n
PI-1259
Olivine + 0.01 Fe–S
6.7 ± 0.4
0.03
0.8
PI-1257
Olivine + 0.09 Fe–S
8.1 ± 0.4
0.08
1.2
PI-1249
Olivine + 0.20 Fe–S
1523
7.3 ± 0.4
0.10
1.0
PI-1279
Olivine + 0.05 Au
4.2 ± 0.3
0.12
1.2
PI-1287
Olivine + 0.20 Au
1471 1471 1471 1521 1521 1521 1523
6±1
0.09
1.1
1508 1519 1519 1519 1519 1523
10 35 16 72 124 10 28 51 100 15 35 6 14 38 80 120 7 14 67 140 36 78 136 17 49 64
boundary, an environment where metallic melt rather than silicate melt is likely to affect the viscosity of the lower mantle. In addition, understanding the interaction of a metallic melt with a silicate mantle is necessary for modeling the initial conditions of core formation. If the core grew by percolation of metallic melt through the mantle (Hustoft and Kohlstedt, 2006), to model accurately this system, it is important to know the effect of a metallic melt on the viscosity of silicate rocks before the core-composition fluids segregated from the silicate mantle (Hier-Majumder et al., 2006).
0.5 1.3 0.5 2.1 3.0 0.5 1.7 3.0 5.4 0.5 1.4 0.7 1.6 3.7 8.4 15 0.6 0.5 2.5 6.1 4.5 11 25 4.5 15 22
formed at constant applied load for a range of differential stress from 5 to 140 MPa and strain rates from 10− 6 to 10− 4 s− 1 at temperatures of 1473 to 1523 K and a
2. Experimental methods Details of the experimental methods are reported in Hustoft and Kohlstedt (2006) and Scott and Kohlstedt (2006); the main points are summarized here. Samples were synthesized from San Carlos olivine (Fo90) with d ≤ 10 μm and reagent grade powders of Fe, FeS, and Au. All powders were pre-dried in a 1 atm furnace at 1273 K for 10 h. Samples of olivine with 0.01, 0.09 and 0.20 Fe–S with Fe:S = 2:1 by volume and 0.05 and 0.20 Au by volume were hot-pressed in a gas-medium apparatus at 1523 K for 4 h prior to deformation. All triaxial compression (pure shear) experiments were per-
Fig. 3. Log–log plot of strain rate versus stress for samples of olivine + Fe–S. The flow law for diffusion creep of melt-free aggregates of olivine (Hirth and Kohlstedt, 2003) is plotted for comparison to the results from samples with Fe–S melt.
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confining pressure of 300 MPa. The total strain in each experiment was limited to ε b 0.15 (Table 1). 3. Experimental results Scanning electron microscopy (SEM) images illustrating the distribution of Fe–S melt before and after deformation are presented in Fig. 1. SEM images revealing the distribution of Au in two deformed samples are shown in Fig. 2. The distribution of the metallic melt phases is not substantially changed by deformation. No significant segregation or preferred orientation of the metallic melt phase develops during our low-strain, compressive-creep experiments; in contrast, pronounced melt segregation and melt preferred orientation form in similar samples deformed to high strains in simple shear (Groebner and Kohlstedt, 2006; Hustoft and Kohlstedt, 2006). Experimental results are plotted as strain rate versus differential stress for samples of olivine + Fe–S and olivine + Au in Figs. 3 and 4, respectively. Best fits to the data yield n = 0.8 to 1.2, indicating that all samples were deformed in the diffusion creep regime. Strain rates were normalized to a common grain size of d = 8 μm and a common temperature of T = 1523 K using Eq. (1) with m = 3 and Q = 375 kJ mol− 1, values appropriate for the diffusion creep regime (Hirth and Kohlstedt, 2003; Zimmerman and Kohlstedt, 2004). In addition, the flow law determined by Hirth and Kohlstedt (2003) for diffusion creep of samples of melt-free olivine (ϕ = 0) with d = 8 μm and T = 1523 K is shown for comparison.
Fig. 5. Viscosity for samples of olivine plus Fe–S and Au melt normalized by the viscosity of melt-free dunite plotted against melt fraction. Values of viscosity are calculated from the data in Figs. 3 and 4; the viscosity for melt-free olivine is from Hirth and Kohlstedt (2003). A least-squares fit of the data to Eq. (2) yields α = 4 ± 1. A least squares fit of the data to Eq. (3) yields k = 1.4. For comparison, viscosity is plotted versus melt fraction based on Eq. (2) with α = 21, a value appropriate for aggregates of partially molten lherzolite and olivine plus MORB (Zimmerman and Kohlstedt, 2004; Scott and Kohlstedt, 2006). The effect of Au melt on viscosity of peridotite is not distinguishable from that of Fe–S melt.
The dependence of viscosity on the fraction of metallic melt is illustrated in Fig. 5. Effective viscosity is plotted versus melt fraction for samples containing molten Fe–S and samples containing molten Au using all the stress–strain rate data from Figs. 3 and 4. The enhancement of viscosity is determined by plotting the ratio of the measured viscosity to the viscosity for a melt-free (ϕ = 0) sample as calculated from Eq. (1). A value of α for samples of olivine + Fe–S and olivine + Au was determined from a least-squares fit to these data using Eq. (2): g/ ¼ expða/Þ g/¼0
ð2Þ
4. Discussion
Fig. 4. Log–log plot of stress versus strain rate for samples of olivine + Au. The diffusion creep flow law for melt-free samples from Hirth and Kohlstedt (2003) is plotted for comparison to the results from samples with Au melt.
The SEM micrographs in Figs. 1 and 2 illustrate that the distribution of molten Fe–S and Au, respectively, in an olivine aggregate is essentially unchanged by lowstrain (ε b 0.15), compressive creep deformation of the samples. In contrast, a significant melt segregation occurs and a pronounced melt preferred orientation develops during large-strain (ε N 1) experiments (Hustoft and Kohlstedt, 2006; Groebner and Kohlstedt, 2006). The stress versus strain rate data for samples of olivine + 20 vol.% of a metallic melt (Fe–S or Au) plot between the flow law for melt-free olivine and the flow law for olivine + 10 vol.% MORB deforming by diffusion creep (stress exponent n ≈ 1). This fact indicates that a metallic
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melt has a significantly smaller effect on strain rate than does a silicate melt, such as MORB. More precisely, the value of α = 4 ± 1 determined from Fig. 5 for samples of olivine plus a metallic melt with h N 60° is approximately one-fifth of the value of α = 21 reported for samples of partially molten lherzolite (Zimmerman and Kohlstedt, 2004) and samples of olivine plus MORB (Scott and Kohlstedt, 2006), both melt-solid systems with h b 60°. The causes for the enhancement in strain rate that results from the presence of a melt phase must be examined to explain this difference. The presence of melt influences the viscosity of a partially molten rock (i) by causing a local enhancement in stress at grain–grain contacts and (ii) by providing a shortcircuit diffusion path (Cooper et al., 1989). The local enhancement in stress at grain boundaries is a result of the reduced contact area between grains due to the presence of melt between grains. Melt does not transmit shear stress; therefore, the local stress felt at a melt-bordered grain– grain contact is increased relative to that experienced at a boundary with no reduction in contact area due to the presence of melt. For samples of olivine plus MORB, both processes are important. In contrast, for samples of olivine plus metallic melt, the metallic melt almost certainly does not act as an effective short-circuit diffusion path because the solubility of olivine in and thus the flux of olivine through the metallic phase will be very small. Therefore, the primary effect of the metallic melt on viscosity will be through its role in enhancing the local stress felt by grains. This stress enhancement effect is significantly smaller for a metallic melt than for a silicate melt because these two types of melt have significantly different wetting geometries. Metallic melts are present as isolated, nearly spherical pockets confined primarily to triple junctions and four-grain junctions, while silicate melts wet all of the triple junctions and some of the grain boundaries even at low values of ϕ. The distribution of the metallic melt throughout the silicate matrix suggests that metallic melts in an olivine aggregate can be modeled as a weak phase distributed throughout a stronger load-bearing network (Tharp, 1983; Hirth and Kohlstedt, 1995). The relationship between the strength of the porous material σφ and the strength of the solid aggregate r0 is expressed by r/ ¼ 1 k/2=3 r0
ð3Þ
where k is an empirically determined constant generally valued between 0.98 and 2.26 (Tharp, 1983; Hirth and Kohlstedt, 1995). With a value of k = 1.4, Eq. (3) yields a good fit to the data in Fig. 5.
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The results of this study indicate that, for melt-solid systems with θ N 60°, strain rate and viscosity are insensitive to dihedral angle. This behavior is very different from that expected for melt–solid systems with θ b 60° for which viscosity is predicted to decrease with decreasing dihedral angle for a given melt fraction (Cooper et al., 1989). Therefore, because the dihedral angle of molten iron sulfide in a silicate matrix decreases with increasing oxygen fugacity (Minarik et al., 1996; Gaetani and Grove, 1999), in a higher oxygen fugacity environment such as the martian mantle (Rubie et al., 2004), the dihedral angle in the olivine + Fe–S system may be b60° such that this metallic melt could produce a significantly larger reduction in viscosity than observed in our experiments. Likewise, the dihedral angle of an Fe–S melt in contact with a high pressure silicate phase, such as perovskite, can approach and even drop below 60° (Minarik et al., 1996; Shannon and Agee, 1998; Takafuji et al., 2004) such that the effect of an Fe–S melt on viscosity will be substantial. 5. Conclusions For a given melt fraction, the presence of a metallic melt has a significantly smaller effect on the viscosity of a partially molten silicate rock than does MORB for the conditions of our experiments (T ≈ 1473 K, P = 300 MPa, f02= Ni:NiO). In the diffusion creep regime, the addition of 10 vol.% MORB melt decreases the viscosity by nearly an order of magnitude, while the addition of 10 vol.% metallic melt decreases the viscosity by less than a factor of 2. For the olivine + metallic melt system, the value of α in the relation is g/ /g/=0 = exp(–a/) is ∼ 1/5th that for the olivine + MORB system. The decrease in viscosity for an aggregate composed of one or more solid phases plus a melt phase at a given melt fraction is controlled by the level of solubility of solid in the melt, and hence the flux of solid through the melt, as well as by the geometry/distribution of the melt. For relatively insoluble systems, the decrease in viscosity due to the presence of a melt phase is low, but still measurable due to local stress enhancement at grain– grain junctions. Therefore, knowledge of the level of solubility of the minerals in the melt combined with information on the melt topology allows for a priori estimation of the viscosity via the parameter α. Acknowledgments We thank Mark Zimmerman for assistance with experiments and discussions. This study was supported
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by NSF grant OCE-0327143 (basalt melt) and NASA PG&G grant NNG04G173G (metallic melts). References Bulau, J.R., Waff, H.S., Tyburczy, J.A., 1979. Mechanical and thermodynamic constraints on fluid distribution in partial melts. J. Geophys. Res. 84 (B11), 6102–6108. Cooper, R.F., Kohlstedt, D.L., 1982. Interfacial energies in the olivine–basalt system, in high-pressure research. In: Akimota, S., Manghnani, M.H. (Eds.), Geophysics, Advances in Earth and Planetary Sciences, vol. 12. Center for Academic Publications, Tokyo, pp. 217–228. Cooper, R.F., Kohlstedt, D.L., Chyung, K., 1989. Solution-precipitation enhanced creep in solid–liquid aggregates which display a non-zero dihedral angle. Acta Met. 37, 1759–1771. Gaetani, G.A., Grove, T.L., 1999. Wetting of olivine by sulfide melt: implications for Re/Os ratios in mantle peridotite and late-stage core formation. Earth Planet. Sci. Lett. 169, 147–163. Groebner, N., Kohlstedt, D.L., 2006. Deformation induced metal melt networks in silicates: implications for core–mantle interactions in planetary bodies. Earth Planet. Sci. Lett. 245, 571–580. Hier-Majumder, C.A., Hustoft, J.W., Solomon, S.C., 2006. Core formation by percolation of iron-rich liquids. Lunar and Planetary Science, vol. XXXVII. Abstract #1329. Hirth, G., Kohlstedt, D.L., 1995. Experimental constraints on the dynamics of the partially molten upper mantle 2. Deformation in the dislocation creep regime. J. Geophys. Res. 100, 15441–15449. Hirth, G., Kohlstedt, D.L., 2003. Rheology of the upper mantle and the mantle wedge: a view from the experimentalists. In: Eiler, J.M. (Ed.), Inside the Subduction Factory, AGU Geophysical Monograph, vol. 138. AGU Press. Holtzman, B.K., Groebner, N.J., Zimmerman, M.E., Ginsberg, S.B., Kohlstedt, D.L., 2003a. Stress-driven melt segregation in partially molten rocks. Geochem. Geophys. Geosyst. 4 (5), 8607. doi:10.1029/2001GC000258 _______________________. Holtzman, B.K., Kohlstedt, D.L., Zimmerman, M.E., Heidelbach, F., Hiraga, T., Hustoft, J., 2003b. Melt segregation and strain partitioning: implications for seismic anisotropy and mantle flow. Science 301, 1227–1230.
Hustoft, J., Kohlstedt, D.L., 2006. Metal-silicate segregation in deforming dunitic rocks. Geochem. Geophys. Geosyst. 7 (Q02001). doi:10.1029/2005GC001048 _______________________. Keleman, P.B., Hirth, G., Shimizu, N., Spiegelman, M., Dick, H.J.B., 1997. A review of melt migration processes in the adiabatically upwelling mantle beneath oceanic spreading ridges. Philos. Trans. R. Soc. Lond., A 355, 283–318. Minarik, W.G., Ryerson, F.J., Watson, E.B., 1996. Textural entrapment of core-forming melts. Science 272, 530–533. Rubie, D.C., Gessmann, C.K., Frost, D.J., 2004. Partitioning of oxygen during core formation on the Earth and Mars. Nature 429, 58–61. Scott, T., Kohlstedt, D.L., 2006. The effect of large melt fraction on the deformation behavior of peridotite. Earth Planet. Sci. Lett. 246, 177–187. Shannon, M.C., Agee, C.B., 1998. Percolation of core melts at lower mantle conditions. Science 280, 1059–1061. Shaw, H.R., Wright, T.L., Peck, D.L., Okamura, R.T., 1968. The viscosity of basaltic magma: an analysis of field measurements in Makaopuhi lava lake, Hawaii. Am. J. Sci. 266, 225–264. Takafuji, N., Hirose, K., Ono, S., Xu, F., Mitome, M., Bando, Y., 2004. Segregation of core melts by permeable flow in the lower mantle. Earth Planet. Sci. Lett. 224, 249–257. Terasaki, H., Kato, T., Urakawa, S., Funakoshi, K., Suzuki, A., Okada, T., Maeda, M., Sato, J., Kubo, T., Kasai, S., 2001. The effect of temperature, pressure, and sulfur content on viscosity of the Fe– FeS melt. Earth Planet. Sci. Lett. 190, 93–101. Tharp, T.M., 1983. Analogies between the high-temperature deformation of polyphase rocks and the mechanical behavior of porous powder metal. Tectonophysics 96, T1–T11. Tucker, D.B., Weisberg, A.H., 1986. Planarization of gold and aluminum thin films using a pulsed laser. IEEE Electron Device Lett. EDL-7, 1–4. Yoshino, T., Walter, M.J., Katsura, T., 2003. Core formation in planetesimals triggered by permeable flow. Nature 422, 154–157. Yoshino, T., Walter, M.J., Katsura, T., 2004. Connectivity of molten Fe alloy in peridotite based on in situ electrical conductivity measurements: implications for core formation in terrestrial planets. Earth Planet. Sci. Lett. 222, 625–643. Zimmerman, M., Kohlstedt, D.L., 2004. Rheological properties of partially molten lherzolite. J. Petrol. 45, 275–298.